📂Fluid Mechanics

Definition of Compressible Fluid

Definition ¹

A fluid whose density is constant is called an incompressible fluid. A fluid that is not incompressible is called a compressible fluid.

Explanation

$$ \nabla \cdot \mathbf{u} = 0 $$ When the velocity is represented as $\mathbf{u}$, the fluid being incompressible is equivalent to satisfying the conservation equation shown above. Of course, being exactly zero is too idealized in the real world; in practice, a fluid is called incompressible when changes in density are small enough to be neglected.

The difference between fluids in terms of compressibility is essentially the difference between liquids (incompressible) and gases (compressible). Of course, liquids can exhibit compressibility under very extreme conditions, but, as noted above, in ordinary situations that compressibility is small enough to be neglected.